Il résulte des généralités sur les formes quadratiques que la classe spinorielle de la trace intégrale d’un corps de nombres détermine la signature et le discriminant du corps. Dans cet article, nous définissons une famille de corps de nombres, qui contient, entre autres, tous les corps galoisiens de degré impair modérément ramifiés, pour lesquels la réciproque est vraie. Autrement dit, pour un corps de nombres de cette famille, on montre que la classe spinorielle de la trace intégrale ne contient pas d’informations sur autres que celles qui sont fournies par le discriminant et la signature.
It follows from generalities of quadratic forms that the spinor class of the integral trace of a number field determines the signature and the discriminant of the field. In this paper we define a family of number fields, that contains among others all odd degree Galois tame number fields, for which the converse is true. In other words, for a number field in such family we prove that the spinor class of the integral trace carries no more information about than the discriminant and the signature do.
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Mots clés : Arithmetic invariants, tame fields, arithmetic equivalence, trace forms.
@article{JTNB_2020__32_3_711_0,
author = {Mantilla-Soler, Guillermo},
title = {An introduction to oddly tame number fields.},
journal = {Journal de th\'eorie des nombres de Bordeaux},
pages = {711--717},
publisher = {Soci\'et\'e Arithm\'etique de Bordeaux},
volume = {32},
number = {3},
year = {2020},
doi = {10.5802/jtnb.1140},
language = {en},
url = {http://archive.numdam.org/articles/10.5802/jtnb.1140/}
}
TY - JOUR AU - Mantilla-Soler, Guillermo TI - An introduction to oddly tame number fields. JO - Journal de théorie des nombres de Bordeaux PY - 2020 SP - 711 EP - 717 VL - 32 IS - 3 PB - Société Arithmétique de Bordeaux UR - http://archive.numdam.org/articles/10.5802/jtnb.1140/ DO - 10.5802/jtnb.1140 LA - en ID - JTNB_2020__32_3_711_0 ER -
%0 Journal Article %A Mantilla-Soler, Guillermo %T An introduction to oddly tame number fields. %J Journal de théorie des nombres de Bordeaux %D 2020 %P 711-717 %V 32 %N 3 %I Société Arithmétique de Bordeaux %U http://archive.numdam.org/articles/10.5802/jtnb.1140/ %R 10.5802/jtnb.1140 %G en %F JTNB_2020__32_3_711_0
Mantilla-Soler, Guillermo. An introduction to oddly tame number fields.. Journal de théorie des nombres de Bordeaux, Tome 32 (2020) no. 3, pp. 711-717. doi : 10.5802/jtnb.1140. http://archive.numdam.org/articles/10.5802/jtnb.1140/
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